Large-Scale First-Principles Electronic Structure Calculations for Nano-Meter Size Si Quantum Dots

Abstract

We have studied the system size dependence of the density of states, band gap, and the charging energy of the large size Si quantum dots of 2.2 to 7.6 nm diameters by first-principles electronic structure calculations. The largest model examined in this study consists of over 10,000 Si atoms, and we performed such large calculations by using recently developed real-space density-functional theory code suitable for massively parallel computers. The density of states of 6 nm-diameter Si quantum dot is almost the same as that of the bulk Si. The band gaps of the Si quantum dots have been calculated by the ∆SCF method with local-density approximation, and we have found that the difference between the ∆SCF band gap and the Kohn-Sham eigenvalue gap is equal to the inverse of the dot radius. Consequently the ∆SCF band gap converges to the Kohn-Sham eigenvalue gap in the infinitely large size limit with the local-density approximation.

Transition between direct and indirect band gap in silicon nanocrystals

“…10 More recently, a number of investigations employed electronic structure calculations at various levels of sophistication, ranging from tight-binding methods, 7,11,12 empirical pseudopotentials, 13 via density functional theory [4][5][6][14][15][16] (DFT), to the GW approximation combined with Bethe-Salpeter equation (BSE) or time-dependent DFT [17][18][19][20] and diffusion Monte Carlo calculations (DMC). 21 These methods have generally confirmed the quantum confinement on an ab initio level and provided valuable insight into the electronic structure and optical properties, although, inevitably the GW, BSE, and DMC methods were limited to rather small Si clusters (<1.5 nm), so that details of the transition from nano-to bulk regime were not accessible.…”